Hi IOSC,
Great question, and a really important point from Keri regarding never soliciting Yelp reviews from your customers. Their policies and filters are the most stringent of any review platform; Yelp wants all reviews to happen spontaneously.
When it comes to Google-based reviews, the best policy is to take it slow. Avoid sending out email blasts or running campaigns that will generate a large number of reviews at any one time. Google has also upped the stringency of their review filters of late and too great a velocity of incoming reviews can result in review loss for the business owner. Ask, perhaps, 1-3 happy customers a week if they'd like to review you. Then, if 1 or 2 of them do, this will be a gentle acquisition.
Also, take a look at your competitors' average number of reviews. If most of them in your locale have, say, 20 Google-based reviews, then aim for having 30 or 40 on your profile...don't aim for having 200. This is another area in which it is speculated that Google may become suspicious that reviews are being bought or falsely generated by the business.
A read through Google's Review Posting Guidelines will be very important for you:
https://support.google.com/places/answer/187622?hl=en
Another good step is to, again, look at your direct local competitors and see which 3rd party review sites Google is linking to from their Google+ Local pages in the 'reviews from around the web' section. This way, you may discover that, for your locale and industry, Google seems to be trusting certain sites like citysearch, judysbook or insiderpages most. This will signal to you that it's important for you to have customers review you there.
In actually setting about requesting reviews, a good process would be to obtain the customer's email at the time of service. Follow up 2-3 days after a service is rendered with a brief, friendly, well-crafted email, letting the customer know how much you would appreciate his review. You might list a few places (not including Yelp) where you have review profiles and let the customer know that you would like them to pick their favorite platform. While Google and Yelp reviews are typically the most important for local business owners, review diversity is very healthy insurance against massive review loss, should you ever lose all of your reviews on one site or another. Remember, not everyone is going to have a Google account, so leaving a Google based review could be a pain for them, whereas if they are an active member at TripAdvisor, their review their will be easy for them and good for your business.
I recommend you read Phil Rozek's 2012 post on the local review ecosystem to get a quick education on the way in which data is shared between some of the review platforms (http://www.localvisibilitysystem.com/2012/07/06/the-local-business-reviews-ecosystem/). Great piece!
Hope I've pointed out some helpful ideas for you here. Just remember, a slow, diverse and steady acquisition of reviews over time is a much better strategy than trying to make a big splash all at once.